1. Field of the Invention
The present invention relates, generally, to the construction of telescope or imaging systems and, more specifically, to systems which use optical elements having shapes and curvatures formed by the bending or stretching of a membrane over an appropriate boundary wherein such membrane assumes a shape that can concentrate electromagnetic radiation.
2. Description of the Prior Art
Known telescope systems typically are formed either with only a single primary optical element or with a combination of a primary element along with other optical elements so as to improve the performance of the overall system. Indeed, if the field of view needs to be larger than that which is afforded by a single primary optical element, subsequent optics (a secondary and tertiary) can be used to correct any aberrations induced by the primary optical element. A number of designs for two and three mirror systems have been developed over the years resulting in systems which have large focal surfaces. See Astronomical Optics, Schroeder 1987. Such systems are typically xe2x80x9con-axisxe2x80x9d, wherein the secondary and tertiary optics obstruct the primary optical element. However, the scattering and diffraction of the incident electromagnetic radiation by both the secondary optics and its support structure reduces the performance of the overall on-axis system. This is particularly problematic for the observation of low-contrast objects as well as in communications systems where cross-talk between nearby antennas is undesirable.
One solution to the aforementioned problem with on-axis designs is to use an off-axis design. Unfortunately, however, the field-of-view of such off-axis designs is generally limited unless steps are taken to control the new set of off-axis aberrations. One known solution to control such off-axis aberrations is to tip the secondary reflector with respect to the primary optical element. As a result, the aberrations induced by the tipped secondary reflector cancel those of the off-axis primary optical element, thus affording a performance which is substantially equal to that of an unobstructed on-axis reflector of the same aperture. Be that as it may, the field-of-view for such a system still has much to be desired. Thus, it can be appreciated that an off-axis system with a wide field-of-view would be desirable in either a telescope or imaging system.
Further, there are problems associated with the construction of precision reflectors. Such problem of constructing precision reflectors (initially for use in telescope mirrors) has a long history tracing back to Gregory (1663), Newton (1668) and Cassegrain (1672). The first successful reflectors using glass substrates with silvered reflecting surfaces were constructed in the late 1850""s by von Steinheil in Germany and Foucault in France. The function of any glass or metal mirror is to act as a substrate providing support for a thin layer of high reflectivity materialxe2x80x94the glass or metal being formable into shapes that have useful optical properties. By examining the areal densities of the reflecting layer and the substrate we find that the current state-of-the-art has much to be desired, wherein a factor of at least 107 in areal density exists between the reflecting surface and the supporting substrate.
The areal density of the reflecting layer is given by
"sgr"m=xcfx81t
with t being the thickness of the reflecting layer, and p the density. The thickness of the reflecting layer of a high electrical conductivity metallic film can be determined, to good approximation for a specific reflecting material, by considering the skin depth       δ    =          1                        πνμσ          e                      ,
where "sgr"e is the conductivity of the reflecting surface, v is the frequency of the electromagnetic radiation, and xcexc is the permittivity of the reflecting surface. For a very good conductor like copper, "sgr"e=5.7xc3x97107 xcexa9xe2x88x921/m and xcexc=1. If we consider a drop in intensity of 106 to be opaque, we find that t=7xcex4. In the case of optical light (xcex=0.5 xcexcm), the film only has to be 50 nanometers thick to reflect the incident light with little loss; for microwaves (xcex=1000 xcexcm), a 1.7 xcexcm thickness is required. For this example, "sgr"mxcx9c2xc3x9710xe2x88x923 g/m2 in distinct contrast to the areal density of the substrate material, which can be many orders of magnitude greater.
Current technology millimetric telescopes have densities of order 10 kg/m2, about a factor of 107 between the reflecting layer""s density and that of the support structure. For optical telescopes, the situation is much worse with the current state of the art having areal densities of order 150 kg/M2 (the NASA 2.5 m HST and the Air Force Starfire 3.5 telescopes). By examining existing telescopes one finds that the mass density of the supporting substrate (generally some form of glass) is
"sgr"mxe2x88x9d(aperture)0.5.
This is independent of the technology used, or the epoch when the telescope was constructed.
By comparison, the areal density of a membrane reflector system scales differently and is straightforward to calculate. For the reflective membrane itself
"sgr"m=xcfx81mt.
For the supporting ring       σ    ⊕    =      -                  4        ⁢                  ρ          ⊕                ⁢                  h          ⁢                      (            d            )                          ⁢        Δ        ⁢                  xe2x80x83                ⁢        d            d      
here h(d) is the functional dependence of the ring""s height on the diameter of the ring, and xcex94d is the width of the ring. The total density is simply the sum   σ  =                    σ        m            +              σ        ⊕              =                            ρ          m                ⁢        t            +                                    4            ⁢                          ρ              r                        ⁢                          h              ⁢                              (                d                )                                      ⁢            Δ            ⁢                          xe2x80x83                        ⁢            d                    d                .            
It is instructive to note two cases, h(d)=h (a constant height ring), and h(d)h=0(d/d0)1/3 (a constant stiffness ring). In the first case, the areal density decreases with aperture as it does for the constant stiffness case. Only if the ring has h(d)=h0(d/d0)xcex1 with xcex1 greater than 1 does "sgr" grow with   σ  =                    ρ        m            ⁢      t        +          4      ⁢                        ρ          ⊕                ⁢                  (                      ho            do                    )                    ⁢                        (                      d            do                    )                          α          -          1                    ⁢      Δ      ⁢              xe2x80x83            ⁢      d      
This is in distinct contrast to the data for current mirrors, which have "sgr"xe2x88x9dd0.5. For larger diameters, the thickness of the membrane can be reduced, since for a given deflection the pressure can be lower. Thus, not only is a membrane reflector less massive to being with, but the areal density can actually decrease with larger apertures if the ring and membrane are chosen correctly.
Clearly, the areal density of a telescope or imaging system could be reduced by large orders of magnitude by constructing only the desired reflective surface and not the heavy supporting structure needed to control the gravitationally induced deformations. To date, however, such design has not been practically implemented. Further, it is not known to use a space curve as a boundary to produce off-axis surfaces that can represent a segment of a conic section. Moreover, the prior art does not provide for the figuring of such a surface by selectively distorting the associated boundary. In addition, there is nothing in the prior art which discusses the re-imaging of an off-axis optical element onto a deformable tertiary so as to correct for non-ideal primary surface shape.
Therefore, the present invention is directed to a method for constructing telescope systems, antenna systems, imaging systems, or other concentrators of electromagnetic radiation having optical elements whose shapes, orientations and locations are specifically chosen to achieve a diffraction limited optical system. The individual optical elements may be constructed by deforming a membrane such that non-symmetric aspherical low-mass surfaces are achieved.
Accordingly, in an embodiment of the present invention, an apparatus for electromagnetic radiation concentration is provided which includes: a peripherally-disposed boundary member, the boundary member having a shape defined as a space curve which closes upon itself and which need not be circular nor planar; and a one-piece membrane stretched over the boundary member and secured with respect thereto, the membrane having both a curved shape and a substantially isotropic thickness and being supported entirely upon the boundary member at outermost edges of the membrane.
In an embodiment, the membrane is pressure-formed to obtain the curved shape and substantially isotropic thickness.
In an embodiment, the curved shape has a zero Gaussian curvature.
In an embodiment, the curved shape has a non-zero Gaussian curvature.
In an embodiment, the membrane is elastically deformed to have the curved shape.
In an embodiment, the membrane is permanently deformed to have the curved shape.
In an embodiment, the curved shape is a biconic form with additional higher order polynomial terms.
In an embodiment, the membrane is formed from a single piece of electro-formed foil.
In an embodiment, the curved shape concentrates reflected electromagnetic radiation to an off-axis region.
In an embodiment, the apparatus further includes: a high electrical conductivity material formed over a surface of the membrane for reflectivity.
In an embodiment, the apparatus further includes: a substantially-circular clamp member, the clamp member positioned in substantially fixed and outwardly-adjacent relation to the boundary member, the clamp member securely holding the membrane in stretched formation over the boundary member.
In an embodiment, the clamp member includes a plurality of interlocking grooves between which outermost edges of the membrane are securely held.
In an embodiment, the apparatus further includes: an adjustment device connected to the boundary member, the adjustment device capable of changing the shape of the boundary member so as to subsequently alter the curved shape of the membrane.
In an embodiment, the clamp member is integrally-formed with the boundary member.
In an alternative embodiment of the present invention, a method of forming an apparatus for electromagnetic radiation concentration is provided which includes the steps of: providing a peripherally-disposed boundary member, the boundary member having a shape defined as a space curve which closes upon itself and which need not be circular nor planar; placing a one-piece, stretchable membrane over the boundary member; securing outermost edges of the membrane with respect to the boundary member; deforming the membrane to effect both a curved shape and a substantially isotropic thickness to the membrane; and supporting the membrane entirely upon the boundary member at the outermost edges of the membrane.
In an embodiment of the method, the curved shape has a zero Gaussian curvature.
In an embodiment of the method, the curved shape has a non-zero Gaussian curvature.
In an embodiment of the method, the step of deforming the membrane includes applying pressure to one side of the membrane.
In an embodiment of the method, the applied pressure is positive pressure.
In an embodiment of the method, the applied pressure is negative pressure.
In an embodiment, the method further includes the step of: maintaining the applied pressure wherein the curved shape of the membrane is elastically maintained.
In an embodiment, the method further includes the step of: removing the applied pressure wherein the curved shape of the membrane is permanently maintained.
In an embodiment, the method further includes the step of: cooling the boundary member after the step of applying pressure so as to cool and rigidize the membrane.
In an embodiment of the method, the curved shape is a biconic form with additional higher order polynomial terms.
In an embodiment of the method, the membrane is formed from a single piece of electro-formed foil.
In an embodiment, the method further includes the step of: applying a high electrical conductivity material over a surface of the membrane for reflectivity.
In an embodiment of the method, the curved shape concentrates reflected electromagnetic radiation to an off-axis region.
In an embodiment, the step of securing outermost edges of the membrane further includes the step of: providing a substantially-circular clamp member, the clamp member positioned in substantially fixed and outwardly-adjacent relation to the boundary member, the clamp member securely holding the membrane in stretched formation over the boundary member.
In an embodiment of the method, the outermost edges of the membrane are securely held between a plurality of interlocking grooves in the clamp member.
In an embodiment, the method further includes the step of: adjusting the shape of the boundary member so as to subsequently alter the curved shape of the membrane.
In an embodiment of the method, the clamp member is integrally-formed with the boundary member.
The present invention thereby offers a number of important advancements to the art of constructing the aforementioned systems, including:
Ultra-low areal densities ( less than 2.5 kg/m2) are possible for the individual elements and hence for the entire systems.
The telescope or imaging system of the present invention can achieve diffraction limited performance by combining the primary optical element with subsequent adaptable optics (a secondary and tertiary) to correct for the aberrations of the primary.
The tertiary is located at a position which is a demagnified image of the primary.
Lower total cost than conventional telescopes, due to lower total mass.
Optical advantages: not segmented, lower scattering, low background primary reflector.
Both axis-symmetric and non-symmetric surfaces are constructable by choosing the appropriate boundary for the membrane. The latter is particularly difficult to fabricate using conventional techniques. An off-axis telescope has major advantages when used for low background observations.
Accordingly, the present invention allows for an optical layout consisting of a large primary optical element that can be formed by the inventive membrane, secondary and tertiary optics, and the structures and surfaces needed to construct the membrane reflector. This combination of secondary and tertiary reflectors provides for both a wide field and the correction of aberrations due to defects in the primary optical element. An additional feature of this design is that the tertiary may be rotated about an axis orthogonal to the optical axis, thereby effecting a change in the observing direction without changing the illumination of the primary optical element. The system""s unique features are: a completely unobstructed optical system, low mass, and the ability to quickly switch from one observing position another by rotating the tertiary.
Additional features and advantages of the present invention are described in, and will be apparent from, the Detailed Description of the Preferred Embodiments and the Description of the Drawing.